A previously published exactly solvable quantum mechanical model is used to calculate the dissociative sticking coefficients for H 2/Cu(111) and O 2/Ag(110). The model well describes the sticking coefficient for incident translational energies significantly higher than the activation threshold. Furthermore, for H 2/Cu(111), the low-energy behaviour is accurately described by allowing the interchannel coupling to depend on the translational energy of the incoming molecule, and then by averaging over a distribution of couplings simulating late activation barriers of different heights.